02 Dr. L. Silberstein on tlie Qiiatitam 



Thus our disturbing function F will be 



Here A, B, C are constants, characterizing the nucleus,, 

 their dimensions being, by (25), those of a squared length, 

 and K is a function of the orientation of OP with respect 

 to the principal axes, to wit, if 77^ 77.2, % be the angles 

 which OP makes with these axes, to which belong A, B, C 

 respectively, 



K=* A cos 2 r) Y + B cos 2 772+ C cos 2 773, 



where, of course, cos 2 77!+ cos 2 772+ cos 2 773 = 1. Thus the 

 disturbing function will be 



ir=|^JA(l-3cos 2 77 1 ) + ^(l-3cos 2 77 2 ) 



+ C(l-3cos 2 77 3 ) },.... (26) 

 j 



for a nucleus of any shape and of any charge distribution 



whatever. 



In particular, for any qxially symmetrical nucleus, with 



say the ^I-axis as axis of symmetry, i. e. with C— B, and 



with 77 written for .77^ the disturbing function of the atomic 



system becomes at once 



' F=^- s (B-A)(3 C o^ v -l), 



which is exactly of the form (13), the squared semi-distance 

 of the two centres, a 2 , being here replaced by 



B-A. 



Thus, as was announced, the set of formulae (21), etc.. 

 continues to hold for any axially symmetrical nucleus. If 

 J3>A, we will say, shortly, that the nucleus is "prolate," 

 and it' A> B, that it is " oblate " (for such it would be in the 

 ordinary geometrical sense of the words if its charge were, 

 for instance, uniformly distributed). In view of these two 

 possibilities, affecting the sign of the perturbational term,, 

 it will be better to rewrite here the generalized equation (21), 

 thus 



7A = ^i 1±7 (»-^)«r • • • (28) 



where 2icRch 



7= —jr- 



A-B 



V2 , . . . (28-1) 



the positive sign to be taken for an oblate, and the negative 



